Tuesday, March 18, 2014

How tall was this pyramid?

Here's a real-life math problem: How tall was our pyramid when it was built? You can see that it has some original stones left toward the bottom, but the upper part is all rubble that would originally have been invisible behind a nice stone facing.

We are working on this question ourselves. Here is what you need to know...first, the base is 26.65 meters on each side. The pyramid has one course of stones with a vertical face (called the "plinth course"), then a series of stones with a steep angle--much steeper than the current slope of the pyramid. Here's a drawing that shows the slope of the stones.

Each course of stones is 48 cm high. The angle of the stones is such that if you draw it on graph paper, the top of the course is 11.5 cm back from where a vertical face would have been. (I never knew how hard it could be to write math problems...). This is shown by the triangle with dotted lines above.

In addition, the face of the pyramid was not smooth...each course was stepped back by about 7 cm on average.

So, you should be able to calculate the original height of the pyramid using all that information. We're working on it too...but let's let the 6th graders (and younger) try this before posting any answers.